|Teoria||4||I semestre||Gloria Menegaz|
|Laboratorio||2||I semestre||Gloria Menegaz|
The course deals with the wavelet transform and its applications in image and signal processing. The WT can be considered as a generalization of the Fourier transform to the time/frequency (or time/scale) analysis domain. Accordingly, it allows to overcome some of the main limitations of the FT as the analysis of transient signals that can be characterized with precisely in both the time and the frequency spaces at the same time. Multiresolution analysis is particularly suitable for natural and biological signals, feature extraction for pattern recognition, denoising and image coding.
The course will be complemented by lab sessions aiming at acquiring the practical instruments that are needed in this framework as well as to solve some basic problems. This will be performed using the Matlab Wavelet toolbox. Classical paper-form exercises could also be performed.
1) Background: overview of mathematical tools
- Fourier transform for signals and images
- Windowed Fourier Transform
2) Wavelets and multiresolution representations
- Introduction to multiresolution theory
- Wavelet bases
- Wavelet families and overcomplete representations
- Fast Wavelet Transform (DWT)
- Extension to multiple dimensions
- Applications in ICT and biomedical frameworks
The exam consists in an oral and a project. The oral will concern multiresolution theory. The project will be assigned during the lab. sessions.
|Teoria||Stephane Mallat||A Wavelet Tour of Signal Processing (Edizione 2)||Academic Press||1999||9780124666061|
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